This note extends the Barro (Journal of Political Economy, Vol. 98 (1990), No. 5 part II, pp. S103–S125) model to a two-period, OLG economy with aggregate uncertainty. We show that the government sizes maximizing average growth and individual welfare in a market economy coincide and are not affected by the introduction of uncertainty. The maximum average growth rate, however, does depend on the aggregate uncertainty, the individuals' risk aversion and how the intertemporal elasticity of substitution compares with one. Individual welfare is lower in the stochastic economy. Failing to include uncertainty overestimates the effect of changes in the government size.